Graded Brauer groups and -theory with local coefficients
Invariant subspaces for grasping internal forces and non-interacting force-motion control in robotic manipulation
This paper presents a parametrization of a feed-forward control based on structures of subspaces for a non-interacting regulation. With advances in technological development, robotics is increasingly being used in many industrial sectors, including medical applications (e. g., micro-manipulation of internal tissues or laparoscopy). Typical problems in robotics and general mechanisms may be mathematically formalized and analyzed, resulting in outcomes so general that it is possible to speak of structural...
Invariants, torsion indices and oriented cohomology of complete flags
Let be a split semisimple linear algebraic group over a field and let be a split maximal torus of . Let be an oriented cohomology (algebraic cobordism, connective -theory, Chow groups, Grothendieck’s , etc.) with formal group law . We construct a ring from and the characters of , that we call a formal group ring, and we define a characteristic ring morphism from this formal group ring to where is the variety of Borel subgroups of . Our main result says that when the torsion index...
K (2)- homology of some infinite loop spaces.
-theory of oriented Grassmann manifolds
-theory of weight varieties.
Karoubi’s relative Chern character and Beilinson’s regulator
We construct a variant of Karoubi’s relative Chern character for smooth varieties over and prove a comparison result with Beilinson’s regulator with values in Deligne-Beilinson cohomology. As a corollary we obtain a new proof of Burgos’ Theorem that for number fields Borel’s regulator is twice Beilinson’s regulator.
K-theory of mapping class groups: general p-adic K-theory for punctured spheres.
K-Theory of Non-Additive Functors of Finite Degree.
L2 Riemannian-Roch Theorem for Elliptic Operators.
On Bott-periodic algebraic K-theory.
Let K*(A;Z/ln) denote the mod-ln algebraic K-theory of a Z[1/l]-algebra A. Snaith ([14], [15], [16]) has studied Bott-periodic algebraic theory Ki(A;Z/ln)[1/βn], a localized version of K*(A;Z/ln) obtained by inverting a Bott element βn. For l an odd prime, Snaith has given a description of K*(A;Z/ln)[1/βn] using Adams maps between Moore spectra. These constructions are interesting, in particular for their connections with Lichtenbaum-Quillen conjecture [16].In this paper we obtain a description...
On nonsingular matrices and Bott periodicity.
On p-adic ?-rings and the K-theory of H-spaces.
On -rings and topological realization.
Positivity and Kleiman transversality in equivariant -theory of homogeneous spaces
We prove the conjectures of Graham–Kumar [GrKu08] and Griffeth–Ram [GrRa04] concerning the alternation of signs in the structure constants for torus-equivariant -theory of generalized flag varieties . These results are immediate consequences of an equivariant homological Kleiman transversality principle for the Borel mixing spaces of homogeneous spaces, and their subvarieties, under a natural group action with finitely many orbits. The computation of the coefficients in the expansion of the equivariant...
Proof of Nadel’s conjecture and direct image for relative -theory
A “relative” -theory group for holomorphic or algebraic vector bundles on a compact or quasiprojective complex manifold is constructed, and Chern-Simons type characteristic classes are defined on this group in the spirit of Nadel. In the projective case, their coincidence with the Abel-Jacobi image of the Chern classes of the bundles is proved. Some applications to families of holomorphic bundles are given and two Riemann-Roch type theorems are proved for these classes.
Quantization commutes with reduction in the non-compact setting: the case of holomorphic discrete series
In this paper we show that the multiplicities of holomorphic discrete series representations relative to reductive subgroups satisfy the credo “quantization commutes with reduction”.
Remarks on flat and differential -theory
In this note we prove some results in flat and differential -theory. The first one is a proof of the compatibility of the differential topological index and the flat topological index by a direct computation. The second one is the explicit isomorphisms between Bunke-Schick differential -theory and Freed-Lott differential -theory.
Report on K-theory for convenient algebras. II.
Representations of étale Lie groupoids and modules over Hopf algebroids
The classical Serre-Swan's theorem defines an equivalence between the category of vector bundles and the category of finitely generated projective modules over the algebra of continuous functions on some compact Hausdorff topological space. We extend these results to obtain a correspondence between the category of representations of an étale Lie groupoid and the category of modules over its Hopf algebroid that are of finite type and of constant rank. Both of these constructions are functorially...